An exhaust system of a vehicle or the like is provided with a catalyst and the like in order to purify environmental pollutants (HC, CO, NOx, and the like) contained in an exhaust gas discharged from its engine. The catalyst has an optimal temperature (active temperature) for activating its purification performance. When starting the engine, the exhaust gas has a low temperature, which takes time to reach the active temperature of the catalyst. Therefore, when the temperature of the exhaust gas is low at the time of starting the engine and the like, a heating device for warming up the catalyst raises the catalyst temperature to the active temperature in a short time. As the heating device, chemical heat storage devices that utilize the reaction heat of chemical reactions have been known. The chemical heat storage devices can cut down energy losses (fuel consumption losses) and warm up the catalyst. Patent Literature 1 discloses a catalyst warm-up device provided with a heat storage material (reaction material) disposed on the outside of a catalyst. This catalyst warm-up device warms up the catalyst by utilizing the reaction heat of a chemical reaction of the heat storage material.